To determine which wave has a larger wavelength, we need to use the formula for the wavelength [tex]\(\lambda\)[/tex] of a wave, which is given by:
[tex]\[
\lambda = \frac{v}{f}
\][/tex]
where:
- [tex]\(\lambda\)[/tex] is the wavelength
- [tex]\(v\)[/tex] is the velocity of the wave
- [tex]\(f\)[/tex] is the frequency of the wave
Let's calculate the wavelength of each wave step-by-step.
### Wavelength of Wave A
1. Given frequency [tex]\(f_A = 10\)[/tex] Hz
2. Given velocity [tex]\(v = 80\)[/tex] m/s
3. Using the formula:
[tex]\[
\lambda_A = \frac{v}{f_A} = \frac{80 \text{ m/s}}{10 \text{ Hz}} = 8 \text{ meters}
\][/tex]
### Wavelength of Wave B
1. Given frequency [tex]\(f_B = 4\)[/tex] Hz
2. Given velocity [tex]\(v = 80\)[/tex] m/s
3. Using the formula:
[tex]\[
\lambda_B = \frac{v}{f_B} = \frac{80 \text{ m/s}}{4 \text{ Hz}} = 20 \text{ meters}
\][/tex]
### Conclusion
- The wavelength of Wave A is 8 meters.
- The wavelength of Wave B is 20 meters.
Comparing the two wavelengths, Wave B has a larger wavelength (20 meters) compared to Wave A (8 meters).
Therefore, Wave B has the larger wavelength.
